Power dissipation generates heat in your circuit and may or may not be a problem depending on the circuit.

For example, you see a lot of posts here that ask "why is my voltage regulator getting hot?". Its because power is dissipated in the regulator due to the voltage across it and the current through it, P = V x I.

If you think about a two-terminal device like reisitor or diode, the curent into one terminal has to be the same like the current going out of the other terminal, hence the current stays the same. If the device had no voltage drop, there would be no power lost like in superconductors.
So when something dissipates power there is a voltage drop somewhere and at the same time there is current flowing through that.

Power may be lost from the circuit's point of view but it's never really lost; it always goes somewhere - heat, light, sound, motion, chemical changes as when charging a battery.

Current and voltage are not really power themselves; they are more like carriers of power. They carry power from a source like a generator or battery to a load, which is another name for a destination of power.